Q. 5 C5.0( 1 Vote )

Solve the following equations :

tan 3x + tan x = 2 tan 2x

Answer :


Ideas required to solve the problem:


The general solution of any trigonometric equation is given as –


• sin x = sin y, implies x = nπ + (– 1)ny, where n Z.


• cos x = cos y, implies x = 2nπ ± y, where n Z.


• tan x = tan y, implies x = nπ + y, where n Z.


given,


tan x + tan 3x = 2tan 2x


tan x + tan 3x = tan 2x + tan 2x


tan 3x – tan 2x = tan 2x – tan x



As, tan (A - B) =





tan x = 0 or tan 2x = 0 or tan 3x = tan x


if tan x = tan y, implies x = nπ + y, where n Z


x = nπ or 2x = mπ or 3x = kπ + x




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